Present article studies the actual questions of combating the acts of terror and the manifestations of terrorism. The author shortly presents the genesis of political legal prohibition on the terrorist acts in the countries of the post-Soviet territory starting from 50s of the last century. Very informative is the data on the type, structure and activity of special services combating terrorism and the comparative legal analysis of the acts on amenability for different forms of that crime in various states are presented: Ukraine, Russian Federation, Latvia, as well as Poland, Bulgaria and some other. The author shares some critical views on too much differentiated approach of these countries to the question of the legal norms towards the terrorist acts. The difference of the attitudes of the legislators in various countries, mainly in Europe, is illustrated when trying to define the object of the crime analyzed and the object of criminal legal protection of the values which are being harmed or may be harmed in the course of an act of terror. At the same time the present article shows the details of criminalization of terrorism by the representatives of parliamentarians in Middle Asia and Far East, especially in Kazakhstan, Kyrgyzstan and China. (Published Abstract)